Finite Group Databasebeta

← #15633724

Subgroups — #15633724

Order 2816.

1870 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082470C211yesmaximal, characteristic, complemented
2#13081369C214yesmaximal, complemented
3#13081334C212yesmaximal, complemented
4#13081323C212yesmaximal, complemented
5#13081276C214yesmaximal, complemented
6#13081265C212yesmaximal, complemented
7#13081251C212yesmaximal, complemented
8#13078975C212yesmaximal, complemented
9#13078941C211yesmaximal, characteristic, complemented
10#13078463C212yesmaximal, complemented
11#13078409C211yesmaximal, characteristic, complemented
12#13078119C212yesmaximal, complemented
13#13078080C211yesmaximal, characteristic, complemented
14#13077551C211yesmaximal, characteristic, complemented
15#13077448C212yesmaximal, complemented
16C2×C4×#4323C211yesmaximal, characteristic, complemented
17C11×#3501C211yesmaximal, characteristic, complemented
18C11×#554—21no—
19C11×#554—22no—
20C11×#554C2214yescomplemented
21C11×#554C2212yescomplemented
22D4×Q8×C11—21no—
23D4×Q8×C11C2212yescomplemented
24C11×#544C2212yes—
25C11×#543—22no—
26C11×#533C2211yescharacteristic
27C11×#533C2211yescharacteristic
28C2×C11×C22⋊Q8—22no—
29C11×#518C2212yes—
30C2×C4×D4×C11C2211yescharacteristic
31C2×#66985C2212yes—
32C22×#4323C2211yescharacteristic
33#10623265—21no—
34#10623257—21no—
35#10623226—22no—
36#10623175—22no—
37#10623158—22no—
38#10623116C2214yescomplemented
39#10623115C2212yescomplemented
40#10623108C2212yescomplemented
41#10623056C2212yes—
42#10623054C2212yes—
43#10623008C2211yescharacteristic
44C2×C4×D44C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46#10622706C2211yescharacteristic, complemented
47#10622706C2211yescharacteristic, complemented
48#10622704C2214yescomplemented
49#10622702C2214yescomplemented
50#10622701C2211yescharacteristic, complemented
51#10622701C2211yescharacteristic, complemented
52#10622701C2214yescomplemented
53#10622700C2214yescomplemented
54#10622700C2212yescomplemented
55#10622697C2212yescomplemented
56#10622681C2212yescomplemented
57#10622681C2212yescomplemented
58#10622681C2214yescomplemented
59#10622680C2214yescomplemented
60#10622679C2214yescomplemented
61#10622679C2214yescomplemented
62#10622676C2214yescomplemented
63#10622637C2212yescomplemented
64#10622637C2212yescomplemented
65Q8×C11⋊C8C2212yescomplemented
66Q8×C11⋊C8C2212yescomplemented
67#10622632C2212yescomplemented
68#10622631C2214yescomplemented
69C4×#4324C2214yescomplemented
70#10622629C2214yes—
71#10622629C2214yes—
72#10622629C2214yescomplemented
73#10622628C2214yes—
74#10622628C2214yes—
75#10622628C2212yescomplemented
76#10622627C2214yescomplemented
77C4×#4323C2212yes—
78C4×#4323C2212yes—
79C4×#4323C2212yes—
80C4×#4323C2212yes—
81C4×#4323C2214yescomplemented
82#10622615C2212yes—
83#10622615C2212yes—
84#10622614C2212yes—
85#10622612C2212yes—
86#10622610C2212yes—
87#10622608C2212yes—
88#10622579C2212yes—
89C2×#66873C2211yescharacteristic
90C2×#66871C2211yescharacteristic
91#10622537C2211yescharacteristic
92C2×C4×C11⋊C8C2211yescharacteristic
93C22×Q8×C11—22no—
94C22×D4×C11C2311yescharacteristic
95C23×C4×C11—21no—
96C2×#4343—22no—
97C2×#4339C2312yes—
98C22×D44C2311yescharacteristic
99C22×C4×D11—21no—
100C11×C4⋊Q8—22no—
101C11×C4⋊Q8D411yescharacteristic
102C11×C4⋊Q8D411yescharacteristic
103C11×C4⋊Q8C2311yescharacteristic
104C11×C4⋊Q8C2311yescharacteristic
105C11×C4⋊Q8C2314yes—
106C11×#125—22no—
107C11×#125D412yes—
108C11×#125C2312yes—
109C11×#125C2314yes—
110C11×C22⋊Q8—22no—
111C11×C22⋊Q8—24no—
112C11×C22⋊Q8—21no—
113C11×C22⋊Q8—21no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8—24no—
116C11×C22⋊Q8—24no—
117C11×C22⋊Q8—24no—
118C11×C22⋊Q8—24no—
119C11×C22⋊Q8—24no—
120C11×C22⋊Q8D412yes—
121C11×C22⋊Q8D412yes—
122C4×Q8×C11—21no—
123C4×Q8×C11—21no—
124C4×Q8×C11C2312yes—
125C4×Q8×C11C2312yes—
126C4×D4×C11—22no—
127C4×D4×C11—22no—
128C4×D4×C11—21no—
129C4×D4×C11—21no—
130C4×D4×C11C2312yes—
131C4×D4×C11C2312yes—
132C4×D4×C11C2314yes—
133C4×D4×C11C2314yes—
134C11×#117C2312yes—
135C11×#117C2312yes—
136C2×C11×C4⋊C4—24no—
137C2×C11×C4⋊C4—22no—
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C22⋊C4—21no—
140C2×C11×C22⋊C4—24no—
141C2×C42×C11C2311yescharacteristic
142#67000—24no—
143#66999—22no—
144C2×#4324C2314yes—
145#66985—28no—
146C2×#4323—24no—
147C2×#4323C2312yes—
148C2×#4323C2312yes—
149C2×#4323C2314yes—
150#66983—21no—
151#66983—21no—
152C2×(C2×D11)⋊C4—21no—
153C2×C4⋊Dic11C2311yescharacteristic
154C2×#4318C2312yes—
155C22×C11⋊C8C2311yescharacteristic
156C22×C11⋊C8C2311yescharacteristic
157#66951—24no—
158#66948—22no—
159#66948—22no—
160#66948—22no—
161#66948—24no—
162#66947—24no—
163#66947—24no—
164#66946—24no—
165#66945—22no—
166#66945—22no—
167C4⋊C4×D11—22no—
168#66935—24no—
169(C22⋊D11)⋊C4—24no—
170#66928C2312yes—
171#66928C2314yes—
172#66927C2311yescharacteristic
173#66927C2314yes—
174C4×D44—21no—
175C4×D44—21no—
176C4×D44—21no—
177C4×D44—21no—
178C4×D44C2312yes—
179C4×D44C2312yes—
180C4×D44C2314yes—
181#66922C2311yescharacteristic
182C4×Dic22C2314yes—
183#66896C2312yes—
184#66896C2312yes—
185#66874C2314yes—
186#66874C2312yes—
187#66874C2312yes—
188#66874C2312yes—
189#66874C2312yes—
190#66873C2312yes—
191#66873C2312yes—
192#66873C2314yes—
193#66873C2314yes—
194#66873C2314yes—
195#66873C2312yes—
196#66873C2312yes—
197#66873C2312yes—
198#66873C2312yes—
199#66872C2314yes—
200#66871C2312yes—
201#66871C2312yes—
202#66871C2314yes—
203C4⋊(C11⋊C8)C2312yes—
204C4⋊(C11⋊C8)C2312yes—
205C4⋊(C11⋊C8)C2314yes—
206C4⋊(C11⋊C8)C2314yes—
207#66867C2314yes—
208C4×C11⋊C8C2311yescharacteristic
209C4×C11⋊C8C2311yescharacteristic
210C4×C11⋊C8C2311yescharacteristic
211C4×C11⋊C8C2311yescharacteristic
212C4×C11⋊C8C2314yes—
213#61325—111nomaximal, Sylow
214C24×C11—21no—
215C23×D11—21no—
216C2×Q8×C11—21no—
217C2×Q8×C11—21no—
218C2×Q8×C11—24no—
219C2×Q8×C11—84no—
220C2×Q8×C11C2×D412yes—
221C2×Q8×C11C2×D412yes—
222C2×D4×C11—21no—
223C2×D4×C11—22no—
224C2×D4×C11#4114yescomplemented
225C2×D4×C11C2412yes—
226C22×C4×C11—21no—
227C22×C4×C11—22no—
228C22×C4×C11—24no—
229C22×C4×C11—24no—
230C22×C4×C11—22no—
231C22×C4×C11—82no—
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2411yescharacteristic
235C2×C22⋊D11—22no—
236C22×Dic11—21no—
237#4343—84no—
238#4339—24no—
239#4339—24no—
240C2×D44—21no—
241C2×D44—21no—
242C2×D44—21no—
243C2×D44—24no—
244C2×D44—24no—
245C2×D44—22no—
246C2×D44—22no—
247C2×D44C2412yes—
248C2×D44C2412yes—
249C2×C4×D11—22no—
250C2×C4×D11—22no—
251C2×C4×D11—22no—
252C2×C4×D11—24no—
253C2×C4×D11—82no—
254C2×Dic22C2412yes—
255C11×C4⋊C4—22no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—24no—
258C11×C4⋊C4—24no—
259C11×C4⋊C4—24no—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—22no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4C2×D412yes—
264C11×C4⋊C4C2×D412yes—
265C11×C4⋊C4C2×D412yes—
266C11×C4⋊C4C2×D414yes—
267C11×C4⋊C4C2×D412yes—
268C11×C4⋊C4C2×D414yes—
269C11×C4⋊C4C2412yes—
270C11×C4⋊C4C2412yes—
271C11×C4⋊C4C2412yes—
272C11×C22⋊C4—22no—
273C11×C22⋊C4—24no—
274C11×C22⋊C4—24no—
275C11×C22⋊C4—22no—
276C11×C22⋊C4—22no—
277C11×C22⋊C4C2×D414yes—
278C42×C11—22no—
279C42×C11C2×D411yescharacteristic
280C42×C11C2×D411yescharacteristic
281C42×C11C2411yescharacteristic
282C42×C11C2411yescharacteristic
283C42×C11C2414yes—
284#4324—28no—
285#4323—24no—
286#4323—24no—
287#4323—28no—
288(C2×D11)⋊C4—22no—
289(C2×D11)⋊C4—22no—
290(C2×D11)⋊C4—22no—
291(C2×D11)⋊C4—22no—
292(C2×D11)⋊C4—24no—
293(C2×D11)⋊C4—24no—
294(C2×D11)⋊C4—24no—
295C4⋊Dic11—21no—
296C4⋊Dic11—21no—
297C4⋊Dic11—21no—
298C4⋊Dic11C2412yes—
299Dic11⋊C4—24no—
300C4×Dic11—24no—
301#4318—24no—
302C2×C11⋊C8—22no—
303C2×C11⋊C8—22no—
304C2×C11⋊C8C2411yescharacteristic
305C2×C11⋊C8C2411yescharacteristic
306C2×C11⋊C8C2411yescharacteristic
307C2×C11⋊C8C2411yescharacteristic
308C2×C11⋊C8C2414yes—
309#3506—111no—
310#3501D1111yescharacteristic, complemented
311#3370—114no—
312#3367—112no—
313#3366—112no—
314#3361—114no—
315#3360—112no—
316#3358—112no—
317#3136—112no—
318#3131—111no—
319#3083—112no—
320#3077—111no—
321#3041—112no—
322#3036—111no—
323#2960—111no—
324#2946—112no—
325C2×C4×D8—111no—
326C23×C11—22no—
327C23×C11—24no—
328C23×C11—81no—
329C23×C11—81no—
330C23×C11C22×D411yescharacteristic
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—42no—
334C22×D11—81no—
335C22×D11—81no—
336Q8×C11—24no—
337Q8×C11—42no—
338Q8×C11—42no—
339Q8×C11—81no—
340Q8×C11—84no—
341D4×C11—24no—
342D4×C11—22no—
343D4×C11C2×#4114yes—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—41no—
349C2×C4×C11—44no—
350C2×C4×C11—84no—
351C2×C4×C11—82no—
352C2×C4×C11—84no—
353C2×C4×C11—81no—
354C2×C4×C11C22×D414yes—
355C2×C4×C11C22×D414yes—
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11C22×D411yescharacteristic
360C2×C4×C11C22×D411yescharacteristic
361C2×C4×C11C2×#4112yes—
362C2×C4×C112−1+412yes—
363C2×C4×C11C2511yescharacteristic
364C22⋊D11—44no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—81no—
368D44—22no—
369D44—22no—
370D44—22no—
371D44—22no—
372D44—42no—
373D44—42no—
374D44—81no—
375D44—84no—
376D44—84no—
377C4×D11—44no—
378C4×D11—44no—
379C4×D11—82no—
380C4×D11—84no—
381Dic22—22no—
382Dic22—22no—
383C11⋊C8—21no—
384C11⋊C8—21no—
385C11⋊C8—24no—
386C11⋊C8—21no—
387C11⋊C8—21no—
388C2×AGL(1,ℤ/8)—112no—
389C22×D8—111no—
390#559—114no—
391#556—112no—
392#555—221no—
393#554—21no—
394#554—22no—
395#554C2×D1112yescomplemented
396#554C2×D1114yescomplemented
397#553—222no—
398#550—112no—
399D4×Q8—21no—
400D4×Q8C2×D1112yescomplemented
401#547—221no—
402#544C2×D1112yes—
403#543—22no—
404#538—222no—
405#535—112no—
406#533C2×D1111yescharacteristic
407#533C2×D1111yescharacteristic
408#532—111no—
409#525—222no—
410C2×C22⋊Q8—22no—
411#520—112no—
412#518C2×D1112yes—
413C2×C4×D4—111no—
414C2×C4×D4C2×D1111yescharacteristic
415#490—114no—
416#489—114no—
417#488—114no—
418#488—112no—
419#488—112no—
420#487—111no—
421#487—111no—
422#486—111no—
423#486—114no—
424#486—111no—
425#479—114no—
426#478—114no—
427#478—114no—
428#477—114no—
429#476—112no—
430#474—112no—
431#474—114no—
432#463—114no—
433#463—114no—
434#463—114no—
435#461—112no—
436#459—112no—
437#459—114no—
438#459—114no—
439#446—112no—
440#446—112no—
441C8×Q8—112no—
442C8×Q8—112no—
443#442—114no—
444#440—114no—
445C4×SD16—114no—
446C4×D8—112no—
447C4×D8—114no—
448C4×D8—112no—
449C4×D8—112no—
450C4×D8—112no—
451#428—112no—
452C2×#107—111no—
453#424—112no—
454#423—111no—
455#418—112no—
456#417—112no—
457#416—112no—
458#416—112no—
459C2×#102—111no—
460C2×#102—111no—
461#405—112no—
462C2×C4×C8—111no—
463C22×C11—21no—
464C22×C11—21no—
465C22×C11—24no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—84no—
469C22×C11#54812yes—
470C22×C11C23×D411yescharacteristic
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—84no—
478C4×C11—21no—
479C4×C11—21no—
480C4×C11—24no—
481C4×C11—21no—
482C4×C11—24no—
483C4×C11—42no—
484C4×C11—42no—
485C4×C11—42no—
486C4×C11#54812yes—
487C4×C11#57612yes—
488C4×C11C22×#4111yescharacteristic
489C4×C11C2×2−1+411yescharacteristic
490Dic11—42no—
491Dic11—42no—
492C2×#41—112no—
493C2×#41—222no—
494C22×Q8—22no—
495C22×D4—111no—
496C22×D4C22×D1111yescharacteristic
497C23×C4—21no—
498C23×C4—221no—
499AGL(1,ℤ/8)—228no—
500C2×SD16—114no—
501C2×D8—112no—
502C2×D8—112no—
503C2×D8—114no—
504C2×D8—224no—
505C2×M16—112no—
506C22×C8—111no—
507C22×C8—111no—
508C4⋊Q8—22no—
509C4⋊Q8—111no—
510C4⋊Q8C22⋊D1111yescharacteristic
511C4⋊Q8C22⋊D1111yescharacteristic
512C4⋊Q8C22×D1111yescharacteristic
513C4⋊Q8C22×D1111yescharacteristic
514C4⋊Q8C22×D1114yes—
515#127—111no—
516#127—114no—
517#126—224no—
518#125—22no—
519#125C22⋊D1112yes—
520#125C22×D1112yes—
521#125C22×D1114yes—
522#124—112no—
523#124—114no—
524#124—224no—
525#123—224no—
526#123—224no—
527C22⋊Q8—22no—
528C22⋊Q8—24no—
529C22⋊Q8—21no—
530C22⋊Q8—21no—
531C22⋊Q8—22no—
532C22⋊Q8—24no—
533C22⋊Q8—24no—
534C22⋊Q8—24no—
535C22⋊Q8—24no—
536C22⋊Q8—24no—
537C22⋊Q8—222no—
538C22⋊Q8C22⋊D1112yes—
539C22⋊Q8C22⋊D1112yes—
540#121—221no—
541#121—221no—
542#121—222no—
543#121—222no—
544#121—222no—
545#121—224no—
546#120—224no—
547C4×Q8—21no—
548C4×Q8—21no—
549C4×Q8—114no—
550C4×Q8C22×D1112yes—
551C4×Q8C22×D1112yes—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—21no—
555C4×D4—21no—
556C4×D4—112no—
557C4×D4—112no—
558C4×D4—114no—
559C4×D4—224no—
560C4×D4—224no—
561C4×D4—221no—
562C4×D4—221no—
563C4×D4—221no—
564C4×D4—221no—
565C4×D4C22×D1112yes—
566C4×D4C22×D1112yes—
567C4×D4C22×D1114yes—
568C4×D4C22×D1114yes—
569#117—222no—
570#117—222no—
571#117C22×D1112yes—
572#117C22×D1112yes—
573C2×C4⋊C4—24no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—111no—
576C2×C4⋊C4—222no—
577C2×C4⋊C4C22×D1111yescharacteristic
578C2×C22⋊C4—21no—
579C2×C22⋊C4—24no—
580C2×C22⋊C4—221no—
581C2×C42C22×D1111yescharacteristic
582#107—112no—
583#107—112no—
584#107—114no—
585#106—114no—
586C4⋊C8—112no—
587C4⋊C8—112no—
588C4⋊C8—114no—
589C4⋊C8—114no—
590#103—112no—
591#103—112no—
592#103—112no—
593#103—112no—
594#103—114no—
595#102—112no—
596#102—112no—
597#102—112no—
598#102—112no—
599#102—112no—
600#102—112no—
601#102—112no—
602#102—112no—
603#102—114no—
604#102—114no—
605#102—114no—
606#97—114no—
607C4×C8—111no—
608C4×C8—111no—
609C4×C8—111no—
610C4×C8—111no—
611C4×C8—114no—
612C2×C11—22no—
613C2×C11—44no—
614C2×C11C2×#54811yescharacteristic
615C2×C11C2×#57611yescharacteristic
616C2×C11#358411yescharacteristic
617D11—82no—
618D11—82no—
619C24—21no—
620C24—221no—
621#41—224no—
622#41—224no—
623#41—884no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—24no—
627C2×Q8—84no—
628C2×Q8—112no—
629C2×Q8C2×C22⋊D1112yes—
630C2×Q8C2×C22⋊D1112yes—
631C2×D4—22no—
632C2×D4—21no—
633C2×D4—112no—
634C2×D4—112no—
635C2×D4—222no—
636C2×D4—222no—
637C2×D4—222no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—224no—
641C2×D4—221no—
642C2×D4—224no—
643C2×D4#434314yescomplemented
644C2×D4C23×D1112yes—
645C22×C4—21no—
646C22×C4—22no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—22no—
650C22×C4—82no—
651C22×C4—221no—
652C22×C4—222no—
653C22×C4—222no—
654C22×C4—224no—
655C22×C4—222no—
656C22×C4—882no—
657C22×C4C2×C22⋊D1111yescharacteristic
658C22×C4C2×C22⋊D1111yescharacteristic
659C22×C4C23×D1111yescharacteristic
660SD16—228no—
661D8—224no—
662D8—224no—
663D8—228no—
664M16—224no—
665C2×C8—111no—
666C2×C8—111no—
667C2×C8—111no—
668C2×C8—111no—
669C2×C8—114no—
670C2×C8—222no—
671C2×C8—222no—
672C4⋊C4—22no—
673C4⋊C4—21no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—22no—
679C4⋊C4—21no—
680C4⋊C4—112no—
681C4⋊C4—221no—
682C4⋊C4—224no—
683C4⋊C4—221no—
684C4⋊C4—221no—
685C4⋊C4C2×C22⋊D1112yes—
686C4⋊C4C2×C22⋊D1114yes—
687C4⋊C4C2×C22⋊D1112yes—
688C4⋊C4C2×C22⋊D1112yes—
689C4⋊C4C2×C22⋊D1114yes—
690C4⋊C4C2×C22⋊D1112yes—
691C4⋊C4C23×D1112yes—
692C4⋊C4C23×D1112yes—
693C4⋊C4C23×D1112yes—
694C22⋊C4—22no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—22no—
698C22⋊C4—22no—
699C22⋊C4—222no—
700C22⋊C4—222no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C22⋊C4—222no—
704C22⋊C4—224no—
705C22⋊C4—222no—
706C22⋊C4C2×C22⋊D1114yes—
707C42—22no—
708C42—224no—
709C42C2×C22⋊D1111yescharacteristic
710C42C2×C22⋊D1111yescharacteristic
711C42C23×D1111yescharacteristic
712C42C23×D1111yescharacteristic
713C42C23×D1114yes—
714C11#6132511yescharacteristic, complemented, Sylow
715C23—22no—
716C23—24no—
717C23—81no—
718C23—81no—
719C23—222no—
720C23—222no—
721C23—442no—
722C23—881no—
723C23—881no—
724C23C22×C22⋊D1111yescharacteristic
725Q8—24no—
726Q8—42no—
727Q8—42no—
728Q8—81no—
729Q8—84no—
730Q8—222no—
731Q8—222no—
732D4—24no—
733D4—22no—
734D4—222no—
735D4—222no—
736D4—222no—
737D4—222no—
738D4—444no—
739D4—442no—
740D4—442no—
741D4—884no—
742D4—881no—
743D4—884no—
744D4C2×#434314yes—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—41no—
750C2×C4—44no—
751C2×C4—84no—
752C2×C4—82no—
753C2×C4—84no—
754C2×C4—81no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—444no—
758C2×C4—444no—
759C2×C4—882no—
760C2×C4—884no—
761C2×C4—881no—
762C2×C4C2×#434312yes—
763C2×C4#6704012yes—
764C2×C4C22×C22⋊D1114yes—
765C2×C4C22×C22⋊D1111yescharacteristic
766C2×C4C22×C22⋊D1111yescharacteristic
767C2×C4C22×C22⋊D1111yescharacteristic
768C2×C4C22×C22⋊D1114yes—
769C2×C4C22×C22⋊D1111yescharacteristic
770C2×C4C22×C22⋊D1111yescharacteristic
771C2×C4C24×D1111yescharacteristic
772C8—221no—
773C8—221no—
774C8—224no—
775C8—221no—
776C8—221no—
777C22—21no—
778C22—21no—
779C22—24no—
780C22—42no—
781C22—42no—
782C22—84no—
783C22—442no—
784C22—442no—
785C22—442no—
786C22—442no—
787C22—442no—
788C22—442no—
789C22—884no—
790C22#1062334812yes—
791C22C23×C22⋊D1111yescharacteristic
792C4—21no—
793C4—24no—
794C4—21no—
795C4—21no—
796C4—24no—
797C4—42no—
798C4—42no—
799C4—42no—
800C4—442no—
801C4—442no—
802C4#1062334812yes—
803C4#1062336612yes—
804C4C22×#434311yescharacteristic
805C4C2×#6704011yescharacteristic
806C2—22no—
807C2—44no—
808C2—882no—
809C2—882no—
810C2C2×#1062334811yescharacteristic
811C2C2×#1062336611yescharacteristic
812C2#1308338711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3501C2
socleC22×C11C23×D4
hypercenter#3501D11
hypocenterC11#61325
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #533 ◁ #3501

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13082470C2semidirect
2. #13081369C2semidirect
3. #13081334C2semidirect
4. #13081323C2semidirect
5. #13081276C2semidirect
6. #13081265C2semidirect
7. #13081251C2semidirect
8. #13078975C2semidirect
9. #13078941C2semidirect
10. #13078463C2semidirect
11. #13078409C2semidirect
12. #13078119C2semidirect
13. #13078080C2semidirect
14. #13077551C2semidirect
15. #13077448C2semidirect
16. C2×C4×#4323C2semidirect
17. C11×#3501C2semidirect
20. C11×#554C22semidirect
21. C11×#554C22semidirect
23. D4×Q8×C11C22semidirect
38. #10623116C22semidirect
39. #10623115C22semidirect
40. #10623108C22semidirect
46. #10622706C22semidirect
47. #10622706C22semidirect
48. #10622704C22semidirect
49. #10622702C22semidirect
50. #10622701C22semidirect
51. #10622701C22semidirect
52. #10622701C22semidirect
53. #10622700C22semidirect
54. #10622700C22semidirect
55. #10622697C22semidirect
56. #10622681C22semidirect
57. #10622681C22semidirect
58. #10622681C22semidirect
59. #10622680C22semidirect
60. #10622679C22semidirect
61. #10622679C22semidirect
62. #10622676C22semidirect
63. #10622637C22semidirect
64. #10622637C22semidirect
65. Q8×C11⋊C8C22semidirect
66. Q8×C11⋊C8C22semidirect
67. #10622632C22semidirect
68. #10622631C22semidirect
69. C4×#4324C22semidirect
72. #10622629C22semidirect
75. #10622628C22semidirect
76. #10622627C22semidirect
81. C4×#4323C22semidirect
224. C2×D4×C11#41semidirect
310. #3501D11semidirect
395. #554C2×D11semidirect
396. #554C2×D11semidirect
400. D4×Q8C2×D11semidirect
643. C2×D4#4343semidirect
714. C11#61325semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130824702
#130813692
#130813342
#130813232
#130812762
#130812652
#130812512
#130789752
#130789412
#130784632
#130784092
#130781192
#130780802
#130775512
#130774482
C2×C4×#43232
C11×#35012
#6132511